Post on 17-Sep-2018
transcript
Synthesis and characterization techniques Chapter - 3
3.1
Chapter 3
Synthesis and characterization techniques
Synthesis and characterization techniques Chapter - 3
3.2
3.1 Synthesis of spinel ferrites
The properties of spinel ferrite are very much sensitive to the preparation
conditions. A number of novel methods have been developed since then for the
preparation of homogenous, fine/coarse grained and high density spinel ferrite.
The preparation methods have been classified as:
(i) Ceramic method
(ii) Wet-chemical method (co-precipitation method)
(iii) Precursor method (Combustion, Sol-gel technique etc)
(i) Ceramic method
This is the conventional powder processing method which is commercially
accepted since it is possible to maintain the stoichiometry of the final product
even in large scale industrial production. In this method, the preparation of spinel
ferrite takes place at about 1000˚C by solid state reaction. The finely grained
powder of the required composition is shaped by pressing and finally sintered to
obtain ceramically prepared spinel ferrite.
The appropriate metal oxides or their salts, which decompose to give
metal oxides are accurately weighed in the desired proportion and mixed
thoroughly. The mixing is usually carried out in liquid suspension (water,
acetone, alcohol or kerosene) in agate mortar and pestle or ball mill. The slurry is
dried or filtered depending upon the suspension medium and then transferred to
ceramic crucibles and pre- sintered in air or oxygen atmosphere.
The pre-sintered powder contains nucleation centres that are mixed
homogeneously using agate mortar and pestle or ball mill, which helps in the
Synthesis and characterization techniques Chapter - 3
3.3
distribution of nucleation centres formed during pre-sintering. The mixing at this
stage determines the size as well as the grain size distribution. An organic binder
like polyvinyl alcohol (PVA) or Carbon tetrachloride (CTC) is often added at this
stage. The sample is then pressed in a suitable die at about 5 to 10×106 kg/m2.
The pressed material is then fired in oxygen or air between 1000˚-1300˚C
depending upon the substitutions in the ferrites. The completion of solid state
reaction gives rise to homogeneous ferrites.
The ceramic method can be briefly described in four steps:
(i) Initial mixing, grinding and pelletizing
(ii) First sintering or pre-sintering
(iii) Regrinding and re-pelletizing
(iv) Final sintering
(ii) Co-precipitation (wet-chemical) method
The preparation of ferrites powders by the co-precipitation method consists of
oxidation by bubbling oxygen gas through an aqueous suspension of hydroxides
of ferrous and other di or trivalent ions after an alkaline solution has been added.
Thus powders with high homogeneity and purity are obtained [1]. In this method,
the starting solution is prepared by mixing required amount of aqueous solutions
of corresponding sulphates/nitrates/chlorates in proper proportions. A solution of
Sodium hydroxide (NaOH) of appropriate molarity (generally about 2M) is used
as a precipitant. It has been suggested that the solubility product constant (Ksp)
[2] of all the constituents is always exceeded when the starting solution is added
into the precipitant. Therefore in order to achieve simultaneous precipitation of
Synthesis and characterization techniques Chapter - 3
3.4
hydroxides, the starting solution (pH < 7) is added to the precipitant and the
suspension (pH > 7) is heated at about 60˚-100˚C and oxygen gas is bubbled
uniformly into the suspension to promote oxidation reaction until all the
precipitates change into the precipitates of ferrites. The samples are filtered,
washed and dried at 200°C under vacuum.
The wet samples when annealed in air at about 1000˚C, exhibit
generally weight loss because of removal of water and hydroxyl ions even after
the prolonged drying process.
The wet-chemical method can be briefly described in five steps:
(i) Preparation of starting solution
(ii) Precipitation of hydroxides
(iii) Oxidation at ≈ 60˚C with stirring
(iv) Filtering and washing the precipitate of ferrites
(v) Drying at 100-200˚C
(iii) Precursor method
This method involves preparing a precursor, which is a solid solution or a
compound containing metal ions in the desired ratio and the decomposition of
precursor to yield the ferrites. Some of the precursor methods used are:
(a) Hydroxide precursor
(b) Carbonate precursor
(c) Oxalate precursor
(d) Hydrazine carboxylate precursor
Synthesis and characterization techniques Chapter - 3
3.5
This method requires low sintering temperature and hence it is possible
to maintain proper stoichiometry and obtain fine particle ferrite. The
disadvantage in this method is that the hydroxides are gelatinous and therefore it
is difficult to handle, filter and wash them. Sometimes the losses of ions like Cu,
Ni occur on complexing with ammonia. The incomplete precipitation may result in
undesired compositions [3].
3.2 Structural and micro- structural characterization
(A) Energy Dispersive Analysis of X-rays (EDAX)
EDAX stands for Energy Dispersive analysis of X-rays. It is sometimes referred
to as EDS analysis. Energy dispersive X-ray spectroscopy is an analytical
technique used predominantly for the elemental analysis or chemical
characterization of a specimen. Being a type of spectroscopy, it relies on the
investigation of a sample through interactions between electromagnetic radiation
and matter, analyzing X-rays emitted by the matter in this particular case. Its
characterization capabilities are due in large part to the fundamental principle
that each element of the periodic table has a unique atomic structure allowing
X-rays that are characteristic of an element's atomic structure to be uniquely
distinguished from each other.
To stimulate the emission of characteristic X-rays from a specimen, an
high energy beam of charged particles such as electrons or protons, or a beam
of X-rays, is focused into the sample to be characterized. At rest, an atom within
the sample contains ground state (or unexcited) electrons situated in discrete
energy levels or electron shells bound to the nucleus. The incident beam may
Synthesis and characterization techniques Chapter - 3
3.6
excite an electron in an inner shell, prompting its ejection and resulting in the
formation of an electron hole within the atom’s electronic structure. An electron
from an outer, higher-energy shell then fills the hole, and the difference in energy
between the higher-energy shell and the lower energy shell is released in the
form of an X-ray. The X-ray released by the electron is then detected and
analyzed by the energy dispersive spectrometer. These X-rays are characteristic
of the difference in energy between the two shells, and of the atomic structure of
the element form which they were emitted.
Principle of EDAX
During EDAX analysis the specimen is bombarded with an electron beam inside
the scanning electron microscope. The bombarding electrons collide with the
specimen atoms own electrons, knocking some of them off in the process. A
position vacated by an ejected inner shell electron is eventually occupied by a
higher energy electron from an outer shell. To be able to do so, however the
transferring outer electron must give up some of its energy by emitting an x-ray.
The amount of energy released by the transferring electron depends on
which shell it is transferring from, as well as which shell it is transferring to.
Furthermore, the atom of very element releases X-rays with unique amounts of
energy during the transferring process. Thus, by measuring the amounts of
energy present in the x-rays being released by a specimen during electron beam
bombardment, the identity of the atom from which the X-rays was emitted can be
established.
Figure 3.1 Elements in an EDX spectrum are identified based on the energy content of the X electrons transfer from a higher one.
The output of an EDAX analysis is an EDAX spectrum. The EDAX
spectrum is just a plot of how frequently an
level. An EDAX spectrum normally displays peak corresponding to the energy
levels for which the most x
peaks are unique to an atom, and therefore corresponds to a single element. The
higher a peak in a spectrum, the more concentrated the element is in the
spectrum
Fig
Construction and working of spectrometer
The essential parts of the Energy Dispersive spectrometer are shown in the
diagram (Figure 3.3).
Synthesis and characterization techniques
Elements in an EDX spectrum are identified based on the energy content of the X-rays emitted by their electrons as these electrons transfer from a higher-energy shell to a lower
The output of an EDAX analysis is an EDAX spectrum. The EDAX
spectrum is just a plot of how frequently an X-ray is received for each energy
level. An EDAX spectrum normally displays peak corresponding to the energy
for which the most x-rays had been received (Figure 3.2) Each of these
peaks are unique to an atom, and therefore corresponds to a single element. The
higher a peak in a spectrum, the more concentrated the element is in the
Figure 3.2 Example of an EDX spectrum.
working of spectrometer
The essential parts of the Energy Dispersive spectrometer are shown in the
Chapter - 3
3.7
Elements in an EDX spectrum are identified based on the energy rays emitted by their electrons as these
energy shell to a lower-energy
The output of an EDAX analysis is an EDAX spectrum. The EDAX
ray is received for each energy
level. An EDAX spectrum normally displays peak corresponding to the energy
) Each of these
peaks are unique to an atom, and therefore corresponds to a single element. The
higher a peak in a spectrum, the more concentrated the element is in the
The essential parts of the Energy Dispersive spectrometer are shown in the
The sample specimen is bombarded with x
generated from the X
sample comprising of various wavelengths according to the various elements
present in the sample is analyzed and various wavelengths are separated on the
basis of their energies by means of a Si (Li) count
(MCA).
Figure 3
The counter produces the pulses proportional in height to the energies in
the incident beam and MCA sorts out the various pulse heights. The excellent
energy resolution of the Si (Li) counter with FET preamplifier and the ability of the
MCA to perform rapid pulse height analysis make the spectrometer to measure
the intensities of all the spectral lines from the sample in about a minute, unless
there are elements in very low concentration are to be determined.
(B) X-ray powder d
When X-ray radiation passes through matter, the radiation interacts with the
electrons in the atoms, resulting in scattering of the radiation. If the atoms are
organized in planes (i.e. the matter is crystalline) and the distances between the
atoms are of the same magnitude
Synthesis and characterization techniques
The sample specimen is bombarded with x-rays of enough high energy
X-ray tube. The fluorescence radiation, emitted by the
sample comprising of various wavelengths according to the various elements
present in the sample is analyzed and various wavelengths are separated on the
basis of their energies by means of a Si (Li) counter and a multichannel
ure 3.3 Energy Dispersive spectrometer.
The counter produces the pulses proportional in height to the energies in
the incident beam and MCA sorts out the various pulse heights. The excellent
energy resolution of the Si (Li) counter with FET preamplifier and the ability of the
d pulse height analysis make the spectrometer to measure
the intensities of all the spectral lines from the sample in about a minute, unless
there are elements in very low concentration are to be determined.
powder diffractometry
n passes through matter, the radiation interacts with the
electrons in the atoms, resulting in scattering of the radiation. If the atoms are
organized in planes (i.e. the matter is crystalline) and the distances between the
atoms are of the same magnitude as the wavelength of the X-rays, constructive
Chapter - 3
3.8
rays of enough high energy
y tube. The fluorescence radiation, emitted by the
sample comprising of various wavelengths according to the various elements
present in the sample is analyzed and various wavelengths are separated on the
multichannel analyzer
The counter produces the pulses proportional in height to the energies in
the incident beam and MCA sorts out the various pulse heights. The excellent
energy resolution of the Si (Li) counter with FET preamplifier and the ability of the
d pulse height analysis make the spectrometer to measure
the intensities of all the spectral lines from the sample in about a minute, unless
there are elements in very low concentration are to be determined.
n passes through matter, the radiation interacts with the
electrons in the atoms, resulting in scattering of the radiation. If the atoms are
organized in planes (i.e. the matter is crystalline) and the distances between the
rays, constructive
and destructive interference will occur.
emitted at characteristic angles based on the spaces between the atoms
organized in crystalline structures called planes. Mos
sets of planes passed through their atoms. Each set of
planer distance and will give rise to a characteristic angle of diffracted
rays. The relationship between wavelength, atomic spacing (d)
solved as the Bragg Equation. If the illuminating wavelength is known (depends
on the type of X-ray tube used and if a monochromator is employed) and the
angle can be measured (with a diffractometer) then the inter
be calculated from the Bragg equation. A set of 'd
compound will be represent the set of planes that can be passed through the
atoms and can be used for comparison with sets of d
standard compounds.
Figure 3.4 Bragg’s law equals to
Diffraction of X-
X-ray beam is equivalent
X-ray beam encounters the regular, 3
of the x-rays will destructively interfere with each other and cancel each other
Synthesis and characterization techniques
and destructive interference will occur. This result in diffraction where X
emitted at characteristic angles based on the spaces between the atoms
organized in crystalline structures called planes. Most crystals can have many
sets of planes passed through their atoms. Each set of planes has a specific inter
r distance and will give rise to a characteristic angle of diffracted
rays. The relationship between wavelength, atomic spacing (d)
solved as the Bragg Equation. If the illuminating wavelength is known (depends
ray tube used and if a monochromator is employed) and the
angle can be measured (with a diffractometer) then the inter plane
ulated from the Bragg equation. A set of 'd-spaces' obtained from a single
compound will be represent the set of planes that can be passed through the
atoms and can be used for comparison with sets of d-spaces obtained from
4 Bragg’s law is satisfied when the inter planer spacing equals to 2dsinθ
-ray beam striking a crystal occurs because the λ of the
equivalent to the spacing of atoms in minerals (1-10 Å).
ray beam encounters the regular, 3-D arrangement of atoms in a crystal most
rays will destructively interfere with each other and cancel each other
Chapter - 3
3.9
in diffraction where X-rays are
emitted at characteristic angles based on the spaces between the atoms
t crystals can have many
planes has a specific inter
r distance and will give rise to a characteristic angle of diffracted X-
rays. The relationship between wavelength, atomic spacing (d) and angle was
solved as the Bragg Equation. If the illuminating wavelength is known (depends
ray tube used and if a monochromator is employed) and the
planer distance can
spaces' obtained from a single
compound will be represent the set of planes that can be passed through the
spaces obtained from
r spacing
ray beam striking a crystal occurs because the λ of the
10 Å). When an
D arrangement of atoms in a crystal most
rays will destructively interfere with each other and cancel each other
Synthesis and characterization techniques Chapter - 3
3.10
out, but in some specific directions they constructively interfere and reinforce one
another. It is these reinforced (diffracted) X-rays that produce the characteristic
X-ray diffraction patterns that used for mineral identification. W.L. Bragg (early
1900's) showed that diffracted X-rays act as if they were "reflected" from a family
of planes within crystals. Bragg's planes are the rows of atoms that make up the
crystal structure.
These "reflections" were shown to occur under certain conditions, which
satisfy the equation:
nλ = 2dsinθ
where, n is an integer (1, 2, 3, ......, n), λ the wavelength, d the distance between
atomic planes, and θ the angle of incidence of the X-ray beam and the atomic
planes. 2dsinθ is the path length difference between two incident X-ray beams
where one X-ray beam takes a longer (but parallel) path because it "reflects" off
an adjacent atomic plane. This path length difference must be equal to an
integer value of the λ of the incident X-ray beams for constructive interference to
occur such that a reinforced diffracted beam is produced. For a given λ of
incident X-rays and inter planer spacing (d) in a mineral, only specific angles (θ)
will satisfy the Bragg equation. For example, on focusing a monochromatic X-ray
beam (X-rays with a single λ on a cleavage fragment of calcite and slowly
rotating the crystal, no "reflections" will occur until the incident beam makes an
angle θ that satisfies the Bragg equation with n = 1. Continued rotation leads to
other "reflections" at higher values of λ and correspond to when n = 2, 3 ... etc;
these are known as 1st, 2nd, 3rd order, etc., "reflections".
Synthesis and characterization techniques Chapter - 3
3.11
Powder Methods: (X-ray beam focused on a powder pellet or powder smeared
on a glass slide). This method is essential for minerals that do not form large
crystals (i.e. clays) and eliminates the problem of precise orientation necessary in
single-crystal methods with its primary application being for mineral
identification. It can also be used to determine mineral compositions
(if d-spacing is a function of mineral chemistry) and to determine relative
proportions of minerals in a mixture. Monochromatic X-rays are focused on pellet
or slide mounted on rotating stage. Since sample is powder, all possible
diffractions are recorded simultaneously from hypothetical randomly oriented
grains. Mount is then rotated to ensure all diffractions are obtained. Older
methods used photographic techniques while most modern applications employ
X-ray powder diffractometers.
X-ray powder diffractometry
Figure 3.5 Photograph of a typical X-ray diffractometer.
X-ray powder diffractometry uses monochromatic X-rays on powder
mounted on glass slide that is attached to a stage which systematically rotates
Synthesis and characterization techniques Chapter - 3
3.12
into the path of the x-ray beam through θ = 0 to 90°. The diffracted x-rays are
detected electronically and recorded on an inked strip chart. The detector rotates
simultaneously with the stage, but rotates through angles = 2θ. The strip chart
also moves simultaneously with the stage and detector at a constant speed. The
strip chart records the intensity of X-rays as the detector rotates through
2θ. Thus, the angle 2θ at which diffractions occur and the relative intensities can
be read directly from the position and heights of the peaks on the strip chart. Use
is then made of the Bragg equation to solve for the inter planer spacing (d) for all
the major peaks and look up a match with JCPDS cards. JCPDS = Joint
Committee on Powder Diffraction Standards.
The X-ray diffractograms were recorded on Philips PW 1710 automated
X-ray powder diffractometer using CuKα radiation, graphite monochromator, and
Xe-filled proportional counter with following specifications.
Scanning rate: 1 degree /minute
Chart speed : 2 cm /minute
The X-ray diffraction patterns were obtained from SICART, Vallabh Vidya
nagar, Gujarat.
The procedure of indexing the X-ray diffractograms, determination of
lattice parameter and X-ray intensity calculations are briefly explained below: In
the case of a cubic lattice,
2
222
2 a
lkh
d
1 ++= (1)
Synthesis and characterization techniques Chapter - 3
3.13
where, a = lattice parameter
d = Inter planer spacing between adjacent planes
(hkl) = Miller indices.
Using Bragg’s law in Equation (1),
( )222
2
2
hkl
2 lkh4a
λθSin ++= (2)
where λ = incident wavelength.
In equation (2) the sum (h2 + k2 + l2) is always an integer while λ2/4a2 is constant
for any one pattern. The equation further suggests that for a particular cubic
crystal, the diffraction takes place at all possible values of Bragg’s angle from the
planes (hkl).
The indices of different planes of a diffractogram for the cubic system can be
derived as:
( ) 2
2
222
2
4a
λ
lkh
θSin=
++ (3)
Lattice parameter ‘a’ can be determined using the formula,
a = N1/2 d (4)
where, N = (h2 + k2 + l2)
In order to determine the cation distribution, X-ray diffraction line intensities were
calculated using the formula suggested by Buerger:
p
2
hklhkl PLFI =
where Ihkl = Relative integrated intensity
Fhkl = Structure factor
Synthesis and characterization techniques Chapter - 3
3.14
P = Multiplicity factor
L = Lorentz-polarization factor
θ = Bragg’s angle
The details are given chapter 4. The Rietveld refinement method
There are six factors affecting the relative intensities of the diffraction lines on a
powder pattern, namely, (i) Polarization factor, (ii) Structure factor, (iii) Multiplicity
factor, (iv) Lorentz factor, (v) absorption factor and (vi) Temperature factor. A
very important technique for analysis is powder diffraction data is the whole
pattern fitting method proposed by Rietveld (1969) [4, 5]. The Rietveld method is
an extremely powerful tool for the structural analysis of virtually all types of
crystalline materials not available as single crystals. The method makes use of
the fact that the peal shapes of Bragg reflection can be described analytically and
the variations of their width (FWHM) with the scattering angle 2θ. The analysis
can be divided into number of separate steps. While some of these steps rely on
the correct completion of the previous one(s), they generally constitute
independent task to be completed by experimental and depending of the issue to
be addressed by any particular experiment, one, several of all these tasks will be
encountered [6].
The parameters refined in the Rietveld method fall into mainly three
classes: peak shape function, profile parameters and atomic and structural
parameters. The peak shapes observed are function of the both the sample (e.g.
domain size, stress/strain, defects) and the instrument (e.g. radiation source,
geometry, slit sizes) and they vary as a function of 2θ. The profile parameters
Synthesis and characterization techniques Chapter - 3
3.15
include the lattice parameters and those describing the shape and width of Bragg
peaks (changes in FWHM and peak asymmetry as a function of 2θ, 2θ
correction, unite cell parameters). In particular, the peak widths are smooth
function of the scattering angle 2θ. It uses only five parameters (usually called U,
V, W, X and Y) to describe the shape of all peaks in powder pattern. The
structural parameters describe the underlying atomic model include the positions,
types and occupancies of the atoms in the structural model and isotropic of
anisotropic thermal parameters. The changes in the positional parameters cause
changes in structure factor magnitudes and therefore in relative peak intensities,
whereas atomic displacements (thermal) parameters have the effect of
emphasizing the high angle region (smaller thermal parameters) or de-
emphasizing it (larger thermal parameters). The scale, the occupancy
parameters and the thermal parameters are highly correlated with one another
and are more sensitive to the background correction than are the positional
parameters. Thermal parameter refinement with neutron data is more reliable
and anisotropic refinement is sometimes possible. Occupancy parameters are
correspondingly difficult to refine and chemical constraints should be applied
whenever possible [7].
Once the structure is known and a suitable starting model is found, the
Rietveld method allows the least-squares refinement [chi-squared (χ2)
minimization] of an atomic model (crystal structure parameters) combined with an
appropriate peak shape function, i.e. a simulated powder pattern, directly against
the measured powder pattern without extracting structure factor of integrated
Synthesis and characterization techniques Chapter - 3
3.16
intensities. With a complete structural model and good starting values of
background contribution, the unit cell parameters and the profile parameters, the
Rietveld refinement of structural parameters can begin. A refinement of structure
of medium complexity can require hundred cycles, while structure of high
complexity may easily require several hundreds. The progress of refinement can
be seen from the resultant profile fit and the values of the reliability factors or R-
values. The structure should be refined to convergence. All parameters (profile
and structural) should be refined simultaneously to obtain correct estimated
standard deviations can be given numerically in terms of reliability factors of R-
values [8]. The weighted profile R value, RWP is defined as,
Rwp =
Σ i wi yi(obs) - yi(calc)
2 / Σ i wi yi(obs)
2 1/2 × 100%
Ideally, the final RWP, should approach the statistically expected R Value, Rexp,
Rexp = ( N - P + C ) /
Σ i wi yi(obs)
2 1/2 × 100%
where, N is the number of observations and P the number of parameters
and C is the number of constraints used in the refinement.. Rexp reflects the
quality of data. Thus, the ratio between the two (goodness of fit),
χ2 = ( Rwp / Rexp )
2 An R value is observed and calculated structure factors, Fhkl, can also be
calculated by distributing the intensities of the overlapping reflections according
to the structural model,
RF = (
Σ hkl
| Fhkl (obs) - Fhkl (calc) | / Σ hkl
Fhkl (obs) ) × 100%
Similarly, the Bragg-intensity R value can be given as,
Synthesis and characterization techniques Chapter - 3
3.17
RI = (
Σ hkl
| Ihkl (obs) - Ihkl (calc) | / Σ hkl
Ihkl (obs) ) × 100%
R values are useful indicators for the evaluation of refinement, especially in the
case of small improvements to the model, but they should not be over
interpreted. The most important criteria for judging the quality of a Rietveld
refinement are (i) the fit of the calculated patterns to the observed data and (ii)
the chemical sense of structural model.
(C) Scanning electron microscopy( SEM)
The SEM was pioneered by Manfred von Ardenne in 1937. The instrument was
further developed by Charles Oatley and first commercialized by Cambridge
Instruments.
Figure 3.6 SEM opened sample chamber.
The scanning electron microscope (SEM) is a type of electron microscope
that creates various images by focusing a high energy beam of electrons onto
the surface of a sample and detecting signals from the interaction of the incident
electrons with the sample's surface. [9, 10]
Synthesis and characterization techniques Chapter - 3
3.18
The type of signals gathered in a SEM varies and can include secondary
electrons, characteristic X-rays, and back scattered electrons. In a SEM, these
signals come not only from the primary beam impinging upon the sample, but
from other interactions within the sample near the surface. The SEM is capable
of producing high-resolution images of a sample surface in its primary use mode,
secondary electron imaging. Due to the manner in which this image is created,
SEM images have great depth of field yielding a characteristic three-dimensional
appearance useful for understanding the surface structure of a sample. This
great depth of field and the wide range of magnifications are the most familiar
imaging mode for specimens in the SEM. Characteristic x-rays are emitted when
the primary beam causes the ejection of inner shell electrons from the sample
and are used to tell the elemental composition of the sample. The back-scattered
electrons emitted from the sample may be used alone to form an image or in
conjunction with the characteristic x-rays as atomic number contrast clues to the
elemental composition of the sample.
In a typical SEM, electrons are thermionically emitted from a tungsten or
lanthanum hexaboride (LaB6) cathode and are accelerated towards an anode;
alternatively, electrons can be emitted via field emission (FE). Tungsten is used
because it has the highest melting point and lowest vapour pressure of all
metals, thereby allowing it to be heated for electron emission. The electron
beam, which typically has an energy ranging from a few hundred eV to 100 keV,
is focused by one or two condenser lenses into a beam with a very fine focal spot
sized 0.4 nm to 5 nm. The beam passes through pairs of scanning coils or pairs
Synthesis and characterization techniques Chapter - 3
3.19
of deflector plates in the electron optical column, typically in the objective lens,
which deflect the beam horizontally and vertically so that it scans in a raster
fashion over a rectangular area of the sample surface. When the primary electron
beam interacts with the sample, the electrons lose energy by repeated scattering
and absorption within a teardrop-shaped volume of the specimen known as the
interaction volume, which extends from less than 100 nm to around 5 µm into the
surface. The size of the interaction volume depends on the electrons' landing
energy, the atomic number of the specimen and the specimen's density. The
energy exchange between the electron beam and the sample results in the
emission of electrons and electromagnetic radiation, which can be detected to
produce an image.
Electronic devices are used to detect and amplify the signals and display
them as an image on a cathode ray tube in which the faster scanning is
synchronized with that of the microscope. The image displayed is therefore a
distribution map of the intensity of the signal being emitted from the scanned
area of the specimen. The image may be captured by photography from a high
resolution cathode ray tube, but in modern machines is digitally captured and
displayed on a computer monitor.
Resolution of the SEM
The spatial resolution of the SEM depends on the size of the electron spot, which
in turn depends on both the wavelength of the electrons and the magnetic
electron-optical system which produces the scanning beam. The resolution is
also limited by the size of the interaction volume, or the extent to which the
Synthesis and characterization techniques Chapter - 3
3.20
material interacts with the electron beam. The spot size and the interaction
volume both might be large compared to the distances between atoms, so the
resolution of the SEM is not high enough to image individual atoms, as is
possible in the shorter wavelength (i.e. higher energy) transmission electron
microscope (TEM). The SEM has compensating advantages, though, including
the ability to image a comparatively large area of the specimen; the ability to
image bulk materials (not just thin films of foils); and the variety of analytical
modes available for measuring the compositions and nature of the specimen.
Depending on the instrument, the resolution can fall somewhere between less
than 1nm and 20nm. The world’s highest SEM resolution is obtained with the
Hitachi S-5500. Resolution is 0.4 nm at 30kV and 1.6 nm at 1 kV.
3.3 Elastic properties
(A) Ultrasonic pulse echo-overlap technique
Introduction
Ultrasonic is the term used to describe the study of all sound like waves whose
frequency is above the range of normal human hearing. Ultrasonic has been with
the living beings from prehistoric days, though the human being had limited
themselves to the primary sense of sound and hearing in the audible almost 200
years ago that dogs could hear sound at frequencies well above the audible
limits (Ultrasonic Sounds) and hence the Galtoris whistle began to be used as a
practical device. The clear recognition that bats use ultrasound for location,
locomotion and communication was however made less than hundred years ago.
The use of ultrasound as a means of locating underwater objects, started at the
Synthesis and characterization techniques Chapter - 3
3.21
time of the First World War, is the beginning of the modern phase of the subject.
Here also if has been recognized that underwater animals like whales, porpoises
and dolphins have been using similar techniques in nature.
Ultrasonic becomes an important tool in physics, a far ranging tool for flaw
detection in engineering, a rival to the x-rays in medical and a reliable method of
underwater sound signaling. Ultrasonic measurement stands as one of the
primary techniques for study of properties of matter such as mechanical,
electromagnetic and particle interaction. The term silent sound also has been
used in the literature to denote ultrasonic waves. Ultrasound (US) is simple
mechanical wave at a frequency above the limit of human hearing. It can be
generated at a board range of frequencies (20 kHz - 10 MHz) and acoustic
intensities. It can be further subdivided into three frequency ranges:
Power US (20 Hz – 100 kHz)
High frequency (100 kHz - 1 MHz)
Diagnostic US (1 MHz - 10 MHz)
US application parameters are given below:
US frequency : more than 20 kHz
US intensity : Power supplied per transducer area, unit (watt/cm2)
US density : Power supplied per sample volume, unit (watt/I)
US dose : Energy supplied per sample volume, unit (J/I)
Generation and detection of Ultrasound
Ultrasonic energy is generated and detected by devices called transducers. By
definition, transducer is a device that transfers power from one system to another
Synthesis and characterization techniques Chapter - 3
3.22
one. In ultrasonic, the most typical conversions are electrical to Ultrasonic energy
(transmitters) or Ultrasonic to electrical energy (receivers). Transducers most
often used for generating ultrasound are piezoelectric, magnetostrictive,
electromagnetic and mechanical devices. Transducers are used for generating
and monitoring ultrasonic waves in different substances viz. gases, liquids and
solids and are at the heart of ultrasonic instrumentation. Several methods can be
used in generating and detecting ultrasonic waves in physical ultrasonic. Few
methods require direct physical contact between the propagating medium and
the ultrasonic source, the best example being piezoelectric transducers. At very
high temperatures and materials that ate highly corrosive and inaccessible, non-
contact transducers are needed. Electromagnetic, Capacitive and Optical
transducers come under this category.
Specimen
Since, the non-parallelism of faces of transducer causes errors in measurement
of attenuation and velocity; therefore the specimen should be optically plane. If
end faces of the sample are nor perfectly (optically) plane and parallel, then a
wave even though originally plane, when reflected, meets the transducers at an
angle. Thus different surface areas of transducer detect different phases of the
wave. The result will be an echo pattern with interface due to interference.
Another error due to improper preparation of sample is called ‘side wall effect’
which results when sample cross-section is comparable to transducer diameter.
This is due to beam divergence.
Synthesis and characterization techniques Chapter - 3
3.23
When ultrasonic waves are passing from liquid to metal in a short distance
at the surface (due to roughness) the sound that passes through liquid lags the
sound which travel through the metal because velocity of sound in liquid is less
than the velocity of sound in metal. In this case the sound wave recombines
inside the material so as to accommodate the difference in travel time. When this
difference in travel time is equal to one half the period of sound wave, a pressure
crest combines with a rarefaction through and the resultant energy is nearly zero
in the metal. The average peak to valley roughness of the surface of specimen
which will cause this destructive interference is called the critical roughness and
is given by:
Rc = λ1 v2 / 2(v2-v1) = λ2 v1 / 2(v2-v1)
where , Rc = critical roughness,
λ1 = wavelength of sound in liquid,
λ2 = wavelength of sound in metal,
v1 & v2 = respective velocities.
Couplant
Though the thickness of couplant (bonding material) is very small (around 0.01
mm) for good coupling it is not entirely negligible compared to the thickness (5 -
10 mm) of many solid specimens used. The purpose of a couplant is to provide a
suitable sound path between the transducer and the test surface. An ideal
couplant effectively wets and totally contacts both surface of transducer and test
part and expel all air between them. It also fills and smooth out irregularities on
the surface of the test part and aids in the movement of the transducer over the
Synthesis and characterization techniques Chapter - 3
3.24
surface. Oil of water is commonly used as a couplant. Grease of heavy oil can be
used on rough and vertical surface.
Transducer
The pulse echo method has to be refined when higher accuracy is needed in
measurements. For instance, in a crystalline solid the velocity depends upon the
direction of propagation. It is important therefore, to select diameter of the
transducer diameter ‘D’ large in comparison with a wave length of the acoustic
wave, one gets a narrow beam of ultrasonic energy with an angular spread φ
given by
Sin φ =1.2 λ / D
where, λ = wavelength of acoustic wave
It is clear that D should be large and φ small to keep bean divergences
small. However if ‘D’ becomes comparable to the lateral dimensions of the
specimen, reflection from the lateral walls of the specimen begin to interfere with
the echo signals which create a serious problem in attenuation measurement.
The ultrasonic propagation characteristic of materials can be determined
using two methods.
1. Continuous wave method and
2. Pulse echo method.
The continuous method, historically the older techniques, uses generally
adopted in KHz regions. For low loss specimen it is possible to achieve high
sensitivities with this method. If specimen thickness were too small to provide
sufficient separation of pulse in pulse echo method, then the continuous wave
method would be better. The pulse method though generally requiring mor
complex instrumentation, overcomes most of the limitations of continuous wave
method and have therefore come into wide spread use, the simplest pulse
method is pulse echo method, where in a transducer is attached to a system (a
solid or a liquid medium)
reflected from the opposite face and be received by transducer itself.
Ultrasonic pulse echo
Figure 3.7 Block diagram of UPT Technique
• Ultrasonic pulses were generated and
longitudinal and shear waves, respectively) 9 MHz PZT transducers.
• The sample was bonded to the transducer using Nonaq stopcock grease.
• The transmit time of the ultrasound was measured upto an accuracy of
1µs using a 100MHz digital storage oscilloscope
• The overall accuracy of these measurements is about 0.25% in velocity
and about 0.5% in elastic moduli.
The periodic motion of a particle about its mean position in a body results
in the vibrational motion of
energy. This transfer of disturbance and hence energy, is called wave motion.
Out of the two possible wave motions, one is perpendicular to the direction of
motion (transverse wave) while the other is p
Synthesis and characterization techniques
method would be better. The pulse method though generally requiring mor
complex instrumentation, overcomes most of the limitations of continuous wave
method and have therefore come into wide spread use, the simplest pulse
method is pulse echo method, where in a transducer is attached to a system (a
solid or a liquid medium) in such a way that the ultrasonic energy can be clearly
reflected from the opposite face and be received by transducer itself.
Ultrasonic pulse echo-overlap Technique
Figure 3.7 Block diagram of UPT Technique
Ultrasonic pulses were generated and detected by X-and Y
longitudinal and shear waves, respectively) 9 MHz PZT transducers.
The sample was bonded to the transducer using Nonaq stopcock grease.
The transmit time of the ultrasound was measured upto an accuracy of
s using a 100MHz digital storage oscilloscope
The overall accuracy of these measurements is about 0.25% in velocity
and about 0.5% in elastic moduli.
The periodic motion of a particle about its mean position in a body results
in the vibrational motion of the adjacent particles due to transfer of mechanical
energy. This transfer of disturbance and hence energy, is called wave motion.
Out of the two possible wave motions, one is perpendicular to the direction of
motion (transverse wave) while the other is parallel to it. The latter are called the
Chapter - 3
3.25
method would be better. The pulse method though generally requiring more
complex instrumentation, overcomes most of the limitations of continuous wave
method and have therefore come into wide spread use, the simplest pulse
method is pulse echo method, where in a transducer is attached to a system (a
in such a way that the ultrasonic energy can be clearly
reflected from the opposite face and be received by transducer itself.
Figure 3.7 Block diagram of UPT Technique.
and Y-cut (for
longitudinal and shear waves, respectively) 9 MHz PZT transducers.
The sample was bonded to the transducer using Nonaq stopcock grease.
The transmit time of the ultrasound was measured upto an accuracy of
The overall accuracy of these measurements is about 0.25% in velocity
The periodic motion of a particle about its mean position in a body results
the adjacent particles due to transfer of mechanical
energy. This transfer of disturbance and hence energy, is called wave motion.
Out of the two possible wave motions, one is perpendicular to the direction of
arallel to it. The latter are called the
Synthesis and characterization techniques Chapter - 3
3.26
longitudinal waves, and they require a medium for their propagation. The waves
falling in the range 20 – 20,000 Hz are called sonic (audible) waves and hence
frequencies above this range are called ultrasonic waves. Ultrasonic waves are
thus a branch of sound waves and it hence exhibits all the characteristic
properties of sound waves. In nature, ultrasonic waves are mechanical vibrations
with different wavelengths, when it is propagated through a medium. The change
in wavelength of ultrasonic waves in different mediums is due to the elastic
properties and the induced particle vibrations in the medium. Further, the
wavelength of the ultrasonic waves is small and hence, exhibits some unique
phenomena in addition to the properties of sound waves.
Types of ultrasonic waves
Based on the mode of propagation, the ultrasonic waves are classified into four
different types that are listed below. These modes are classified according to the
type of vibration of the particles in the medium with respect to the direction of
propagation off the initial waves.
(a) Longitudinal or Compressional waves
(b) Transverse or Shear waves
(c) Surface or Rayleigh waves and
(d) Plate of Lamb waves
(a) Longitudinal or Compressional waves
As the name suggests, the particle motion is along the direction of propagation of
the incident wave. Due to the vibrations of the particle, alternate compressional
and rarefractional zones are produced. The mechanism of propagation for
ultrasonic waves is same as that of ordinary sound waves in air, but instead of
Synthesis and characterization techniques Chapter - 3
3.27
the air molecules it is the atoms of the material under consideration that perform
compression and rarefactions. The resulting propagation of disturbance at
speeds more than that of sound is called longitudinal (compressional) ultrasonic
waves. Because of the compression and rarefaction (dilation of pressure)
processes present in the material, pressure is developed in the material, and
hence these are also called pressure (or dilational) waves. The longitudinal
waves that can propagate in solids, liquids and gases, are easy to generate,
detect and convert into other modes of vibrations. The representation of
longitudinal waves diagrammatically is difficult and is hence avoided. The velocity
of all the types of the modes of propagation is independent of the frequency of
the waves and the dimensions of the material. The velocity of the ultrasonic wave
of any kind can be determined from the elastic moduli, density and Poisson’s
ration of the material.
The longitudinal wave velocity (VL) and Young’s modulus (Y) of the
material is related as,
1/2
Lσ)2σ)(1ρ(1
σ)Y(1V
−+−
=
where, ρ is the density of material (kgm-3) and σ is the Poisson’s ratio
(b) Transverse or Shear waves
Here the vibrations of the atoms of the material considered are perpendicular
(transverse) to the direction of propagation of the ultrasound and hence the
name. Here the forces generated due to propagation of the waves are transverse
or shear to vibrations of the atoms and hence these are also called Shear waves.
Because of these transverse forces, the rate of energy dissipation is much more
Synthesis and characterization techniques Chapter - 3
3.28
than that for longitudinal waves. Consequently, velocity of the shear waves is
approximately half as that of the longitudinal waves in the same material. Shear
ultrasonic waves can pass only through solids and cannot be generated in liquids
or gases. This is because, the mean distance between the atoms of liquids and
gases is so large compared to solids that vibrations of one atom are not readily
transferred to the neighboring atoms and hence the shear waves are attenuated
exceedingly fast. For example, even for highly viscous liquids such as lubrication
oils, the shear ultrasonic waves can travel a very short distance of the order of a
millimeter. The expression for the velocity of transverse waves is,
+=
σ)(1 ρ 2
YVT
1/2
Tρ
GV
=
where, G is the rigidity modulus (Nm-2).
(c) Surface or Rayleigh waves
Lord Rayleigh (1885) demonstrated that waves can propagate over the plane
boundary between an elastic half space and vacuum or sufficiently rarefied
medium (e.g. air). The particle motion is elliptical and amplitude of the waves
decays rapidly with the depth of propagation of the wave in the medium.
(d) Plate or Lamb waves
These types of waves were first described by Horace Lamb in 1916 theoretically
and are hence named in his honour. Simply put, when the surface wave is
introduced into a material, having thickness equal to three times the wavelength
or less, a different kind of wave called plate or lamb waves. During the existence
of the plate wave, the material begins to vibrate as plate i.e. the wave
Synthesis and characterization techniques Chapter - 3
3.29
encompasses the entire thickness of the material. Thus, velocity of these waves
not only depends on the material type but also on the material thickness unlike
the other type of waves.
Elastic Properties
Ultrasonic waves are strain waves that propagate through a solid. The velocity of
longitudinal and transverse elastic waves thus produced is a characteristic
feature of the solid. As discussed, in a longitudinal wave, the material is
alternately compressed and rarefied as one travels along the direction of wave
propagation. In a transverse wave, the material is transversely stressed or
sheared in alternating directions as one travels along the direction of wave
propagation. The transverse wave displaces layers of material perpendicular to
the direction of propagation. The layers are displaced from side to side or they
are displaced up and down.
Figure 3.8 Propagation of elastic waves through materials.
Synthesis and characterization techniques Chapter - 3
3.30
The basic idea is that if there is any distortion of the solid from its equilibrium
shape, (Figure 3.8) the average separation of the atoms within the solid is no
longer optimal. Some atoms will be too close to their neighbours, and some too
far apart. In either case there will be a restoring force, which will act to return the
atoms to their equilibrium separations. The dynamics of the elastic wave will be
affected by the way the solid responds to the restoring force. The two factors
most critical in determining this response are the restoring force per unit
displacement (the natural ‘springiness’ of the substance), and the density of the
substance.
The restoring force on a small region of a solid depends on the type of
distortion (strain) that has taken place during synthesis process. The
parameters that describe the restoring force per unit strain are known as the
elastic moduli of a substance. In the present work we have employed ultrasonic
pulse transmission technique as a tool to get idea about such stress/strain ratio
by measuring longitudinal and transverse wave velocities.
Young’s modulus (E)
This characterizes the restoring forces appropriate to longitudinal extensions of a
substance. In Figure 3.9 shown below, opposite shows two rigid planes of area A
separated in equilibrium by a distance a and held together by ‘springs’
(analogous to planes within a solid held together by atomic bonds).
Figure 3.9 Changing length of sample due to mutu acting on the solid
Young’s modulus is defined by:
a
∆xE
A
F=
where, F is the force exerted on each plane. Notice that, if a rod of material is
stretched in this way, it will tend to ‘neck’ i.e. its
reduced (Figure 3.10). This tendency is characterized by the Poisson ratio,
a substance. If we apply a stress S
induce stress Sy in the y
x
y
S
Sσ =
Figure 3.10 Illustration of the way in which a rod or material necks and bulges as a compressive sound wave travels along rod.
Synthesis and characterization techniques
Changing length of sample due to mutually opposite forces acting on the solid.
Young’s modulus is defined by:
where, F is the force exerted on each plane. Notice that, if a rod of material is
stretched in this way, it will tend to ‘neck’ i.e. its cross-sectional area will be
). This tendency is characterized by the Poisson ratio,
a substance. If we apply a stress Sx (force per unit area) in the
in the y-direction. The Poisson ratio is defined as:
Figure 3.10 Illustration of the way in which a rod or material necks and bulges as a compressive sound wave travels along
Chapter - 3
3.31
ally opposite forces
where, F is the force exerted on each plane. Notice that, if a rod of material is
sectional area will be
). This tendency is characterized by the Poisson ratio, σ, of
x-direction, we
ed as:
Figure 3.10 Illustration of the way in which a rod or material necks and bulges as a compressive sound wave travels along a long thin
Synthesis and characterization techniques Chapter - 3
3.32
Shear or rigidity modulus (G)
This characterizes the restoring forces appropriate to shear or transverse
deformations of the substance. Figure 3.11 opposite shows two rigid planes of
area A held together by ‘springs’ (analogous to planes within a solid held
together by atomic bonds). The rigidity modulus is defined by:
GθA
F=
where F is the force on each plane.
Figure 3.11 Torsion (θθθθ) produced in the solid due to tangential forces.
Bulk modulus (B)
Here it should be noted that the bulk modulus (and its inverse, the compressibility
K) describes the restoring forces appropriate to volume compressions of the
substance. It is defined by:
V
PVB∂
∂−=
where, P is the pressure and V is the volume of the substance.
If the material is easily compressed or easily sheared, than for a given
strain, the restoring force will be small. In other words, a high modulus (E, G, or
Synthesis and characterization techniques Chapter - 3
3.33
B) indicates that the corresponding deformation of the solid is difficult and the
solid has a strong tendency to ‘spring’ back to its equilibrium position.
Poisson’s ratio (σσσσ)
Poisson’s ratio (σ) is the ratio of transverse contraction strain to longitudinal
extension strain in the direction of stretching force. Tensile deformation is
considered positive and compressive deformation is considered negative. The
definition of Poisson’s ratio contains a minus sign so that normal materials have
a positive ratio.
Virtually, all common materials become narrower in cross section when
they are stretched. The reason why, in the continuum view, is that most materials
resist a change in volume as determined by the bulk modulus K more than they
resist a change in shape, as determined by the shear modulus G. In the
structural view, the reason for the usual positive Poisson’s ratio is that inter-
atomic bonds realign with deformation.
The theory of isotropic elasticity allows Poisson’s ratios in the range from
–1 to 1/2. Physically the reason is that for the material to be stable, the stiffness
must be positive; the bulk and shear stiffness are interrelated by formulae which
incorporate Poisson’s ratio.
Synthesis and characterization techniques Chapter - 3
3.34
Elastic Constants
Relationships between various elastic constants
Young’s Modulus E=
G3λ+2Gλ+G
E=λ1+υ(1-2υ)
υ
E=9K(K-λ)
3K-λ
E=2G1+υ E=
9KG
3K+G
E=3K(1-2υ)
Poisson’s Ratio υ=
λ
2(λ+G)
υ=(E+λ)2+8λ2-(E+λ)
4λ
υ=λ
3K-λ
υ=E-2G
2G
υ=3K-2G
2(3K+G)
υ=3K-E
6K
Shear Modulus
G=(E+λ)2+8λ2+(E-3λ)
4
G=λ(1-2υ)
2υ
G=3(K-λ)
2
G=E
21+υ
G=3EK
9K-E
G=3K(1-2K)
21+υ
Bulk Modulus K=
3λ+2G
3
K=(E+λ)2+8λ2+(3λ+E)
6
K=λ1+υ3υ
K=GE
3(3G-E)
K=2G1+υ3(1-2υ)
K=2G1+υ3(1-2υ)
K=E
3(1-2υ)
Synthesis and characterization techniques Chapter - 3
3.35
The inter relationship between various elastic constants are given above.
The knowledge of any two elastic moduli will suffice to give the values of the
remaining elastic constants. Here, it is important to note that Bulk modulus,
rigidity modulus and Young’s modulus are measure in dynes/cm2 (CGS unit
system), Newton/m2 (MKS unit system), or Pascal (SI unit system), while ‘σ’ is a
unit less quantity. The values of elastic moduli for different materials taken from
various sources are given in Table 3.1.
Table 3.1 Bulk modulus (B) Young’s modulus (E), rigidity modulus (G) and
Poisson’s ratio (σσσσ) for typical metals, materials and polycrystalline compositions.
Formula B (GPa) E(GPa) G(GPa) σσσσ
Aluminum 75.5 69 25 0.33
Copper 137.8 110 46 0.34
Magnesium 44.7 45
Nickel 186.0 45 17 0.31
India rubber - 0.48-1.52 0.0016 0.46-0.49
CoFe2O4 179.4 - - -
Mg Fe2O4 110.1/149.2 190.8 74.1 -
Ni Fe2O4 194.4 177.3 68.0 -
Cu Fe2O4 168 174.0 66.0 0.33
Zn Fe2O4 145 184.3 72.0 0.27
Fe Fe2O4 177.2 - -
Li0.5Fe2.5O4 179.0 173 65 0.34
MgAl2O4 - 62.7 - -
Y3Fe5O12 128.99 145.09 58.33 -
YBa2Cu3O7-8 49.38 (205K) 92 39.85(205 K) -
Synthesis and characterization techniques Chapter - 3
3.36
3.4 Magnetic Properties
(A) Physical Property Measurements System (PPMS)
The Quantum Design PPMS represents a unique concept in laboratory
equipment: an open architecture, variable temperature-field system, designed to
perform a variety of automated measurements. Use the PPMS with specially-
designed measurement options, or easily adapt it to our own experiments.
Sample environment controls include fields up to ± 16 Tesla and temperature
range of 1.9 - 400 K
The key features of PPMS used for magnetic measurements are listed below:
Sealed sample chamber with 2.6 cm diameter sample access.
Ever Cool-II – cryogen-free cooling technology.
Versatile sample mounts couple easily to the 12 electrical leads built into
the cryostat insert.
The PPMS is controlled by the Model 6000, a sophisticated
microprocessor-controlled device that eliminates the need to use or
purchase external bridges, current or voltage sources, or lock-in
amplifiers.
Continuous Low-Temperature Control – maintains temperature below
4.2 K for indefinite periods of time and offers smooth temperature
transitions when warming and cooling through 4.2 K.
Temperature Sweep Mode.
User Experiments – External instruments may be controlled automatically
using an integrated Visual Basic interface within our Windows-based
Synthesis and characterization techniques Chapter - 3
3.37
MultiVu control software or by controlling external Visual C++, Delphi or
Visual Basic programs In addition, Grapher utility displays data as it is
being collected.
The PPMS can be used to record various physical properties such as:
(i) Heat Capacity
(ii) AC resistivity
(iii) Thermal conductivity
(iv) Seebeck Coefficient
(v) Thermoelectric figure of merit
(vi) Vibrating sample magnetometer
(vii) AC susceptibility and DC magnetization
(viii) Torque magnetometry
(ix) DC resistivity
Much of the versatility of the PPMS is based on the design of the PPMS
probe. The probe incorporates the magnet, the temperature control, and the
sample puck connector. Figure 3.12 shows typical sample / PPMS probe.
Synthesis and characterization techniques Chapter - 3
3.38
Typical Sample Probe
Figure 3.12 The cross-sectional enlarged PPMS sample chamber.
Synthesis and characterization techniques Chapter - 3
3.39
Sample mounting
The PPMS sample-mounting system is the most interesting and unique feature of
this instrument. At the bottom of the sample chamber is a 12-pin connector pre-
wired to the system electronics. This connector allows you to plug in a removable
sample insert or sample “puck” (Figure 3.13) and offers convenient access to
electrical leads for application hardware and electronics. This connector provides
the foundation for all of the PPMS measurement inserts.
Figure 3.13 Specialized pucks, 2.4 cm in diameter, are used for different measurement applications.
Open architecture The tremendous flexibility of the PPMS allows to interface third-party instruments
to the PPMS hardware. The PPMS MultiVu software supports linking capabilities,
so one can write own programs in Delphi, C++, or Visual Basic to synchronize
PPMS functions with the activity of other instruments to perform custom
experiment. The Model 6000 PPMS Controller houses and controls all the critical
components of the instrument to provide direct communication with the
application electronics for rapid data acquisition.
Synthesis and characterization techniques Chapter - 3
3.40
Temperature control operation
To control the temperature, a vacuum pump draws helium into the annular region
where heaters warm the gas to the correct temperature. This design reduces
thermal gradients and increases system flexibility by making the sample chamber
a controllable environment.
The temperature control system offers the following features:
• Temperature sweep capability allows measurements to be taken while
sweeping the temperature at a user-defined rate (0.01–6 K/min.).
• Continuous Low-Temperature Control (CLTC) ensures precise temperature
control, uninterrupted operation below 4.2 K, and smooth transitions through the
4.2 K helium
boiling point.
• Temperature range of 1.9–400 K accommodates many different types of
measurements.
Field control
The PPMS can be configured with a 7 to 16 Tesla longitudinal magnet or a 7
Tesla transverse magnet. The low noise, bi-polar power supply allows continuous
charging through zero field with current compensation and over-voltage
protection.
Magnetometry
Magnetometry applications are used in conjunction with the automated
temperature and field control capability of the PPMS. The result is a powerful,
Synthesis and characterization techniques Chapter - 3
3.41
fully automated Magnetic measurement workstation that includes integrated
software.
AC/DC Magnetization
The AC measurement system (ACMS) provides the capability to perform both AC
susceptibility and extraction DC magnetization measurements without changing
hardware (Figure 3. 14)
.
Figure 3.14 The servo-motor, coilset, and sample rod for the ACMS. Features • A single automated measurement sequence can perform both AC and DC
magnetization measurements.
• Direct measurement of the instrumental phase shift, not available on any other
AC susceptometer: This feature uses integrated, low inductance calibration coils
to measure and subtract background phase shifts prior to every AC
measurement point.
• High-speed digital filtering: By using a DSP chip, the ACMS improves the
signal-to-noise ratio over analog filters to offer excellent performance over a wide
frequency range.
Synthesis and characterization techniques Chapter - 3
3.42
• A compensation coil reduces environmental noise in AC susceptibility
measurements.
Specifications Temperature range: 1.9-350 K AC frequency range: 10 Hz to 10 kHz AC field amplitude range: 2 mOe to 15 Oe Sensitivity range: DC magnetization measurements: 2.5 x 10-5 emu to 5 emu
(2.5 x 10-8 Am2 to 5 x 10-3 Am2)
AC susceptibility measurements: 2 x 10-8 emu (2 x 10-11 Am2 @ 10 kHz)
Figure 3.15 Photograph of Physical Property Measurement System.
Synthesis and characterization techniques Chapter - 3
3.43
(B) AC Susceptibility
The measurement of magnetic susceptibility is very useful technique to obtain
much important information regarding physical, chemical and magnetic states of
the substance.
The ratio of induced magnetization to the applied magnetic field is known
as magnetic susceptibility. Therefore,
K = M/H emu/cm3
Since M is the magnetic moment of the material per cm3, H is the applied
magnetic field, K also refers to unit volume and is sometimes called the volume
susceptibility.
The thermal variation of low field ac susceptibility gives information
regarding transition temperature, type of magnetic ordering of the substance.
The mass susceptibility related to the volume susceptibility is defined as,
χ = K/ρ’ = M/Hρ emu/g.Oe
where , ‘ρ’ being the density of the material.
The thermal magnetic studies like temperature variation of low field ac
susceptibility play a key role in the study of spin glass behavior. The cusp at
freezing temperature Tf in the low field ac susceptibility versus temperature
characterizes the spin glass behavior [11]. It is also useful to invoke grain size
effects. For example, a very fine stable single domain (SD) particle becomes
superparamagnetic (SP) on heating to temperature several degrees below the
Curie temperature [12]. At an applied magnetic field H, the temperature at which
the susceptibility becomes infinite (i.e. the sample has spontaneous
Synthesis and characterization techniques Chapter - 3
3.44
magnetization), is known as Curie or Neel temperature. At the transition
(ferrimagnetic to paramagnetic) tailing effect is observed, which is due to the
short range spin ordering (spin clusters).
It is obvious that the susceptibility (χ) is directly proportional to the
magnetic moment M and inversely proportional to coercivity HC when the thermal
energy equals to the volume energy of a single domain (SD) particle it becomes
super paramagnetic (SP) and spontaneously fluctuate between their easy
directions yields zero coercivity and as a result the peak is observed in the low
field χ versus T curve [13].
Figure 3.16 Photograph of AC Susceptibility measurement setup.
The ac susceptibility measurements of powdered samples were obtained
using the instrument which consists of (i) magnetic field unit , (ii) magnetization
unit and (iii) temperature unit (Figure 3.16 ) supplied by Magneta, Mumbai, India
[14]. The block diagram of the susceptibility instrument is shown in (Figure 3.17).
The double coil set-up (Halmholtz coil,) operating at a frequency of 263 Hz
produced magnetic field between 0 to 10 kOe. The two coils are oppositely
wound relative to each other producing uniform magnetic field along the axis
perpendicular to the coils. A pick
coil for the magnetization measurements.
Figure 3.17 Block cum circuit diagram of susceptibility
A furnace, platinum wire wound on a silica tube, was used to heat the
sample. A glass jacket with a provision of water circulation is used to avoid
overheating of the coils. The furnace is inserted in a glass jacket and the glass
jacket is placed in the center of the pick
Platinum-Rhodium thermocouple calibrated against the current in the heating
element. Variable current was provided to the heating element by a variable
power supply.
The sample tube is held in the middle of the pick
change in magnetization of the sample. By applying the current to the Halmholtz
Synthesis and characterization techniques
wound relative to each other producing uniform magnetic field along the axis
perpendicular to the coils. A pick-up coil is provided at the center of Halmholtz
coil for the magnetization measurements.
Block cum circuit diagram of susceptibility
A furnace, platinum wire wound on a silica tube, was used to heat the
sample. A glass jacket with a provision of water circulation is used to avoid
overheating of the coils. The furnace is inserted in a glass jacket and the glass
jacket is placed in the center of the pick-up coil. The temperature was sensed by
Rhodium thermocouple calibrated against the current in the heating
e current was provided to the heating element by a variable
The sample tube is held in the middle of the pick-up coil to sense minor
change in magnetization of the sample. By applying the current to the Halmholtz
Chapter - 3
3.45
wound relative to each other producing uniform magnetic field along the axis
up coil is provided at the center of Halmholtz
set-up.
A furnace, platinum wire wound on a silica tube, was used to heat the
sample. A glass jacket with a provision of water circulation is used to avoid
overheating of the coils. The furnace is inserted in a glass jacket and the glass
The temperature was sensed by
Rhodium thermocouple calibrated against the current in the heating
e current was provided to the heating element by a variable
up coil to sense minor
change in magnetization of the sample. By applying the current to the Halmholtz
Synthesis and characterization techniques Chapter - 3
3.46
coil, the change in magnetization of the sample producing emf in the pick-up coil.
The signal is then digitized by an analog to digital converter and then fed to a
digital power meter.
Merits
(1) This instrument can measure at room temperature magnetization of 10
Oe. This means that this even weakest paramagnetic sample in 100 mg
quantity can be measured with an accuracy of 2%.
(2) This instrument can be used to determine Curie temperature.
(3) The electronic unit of this instrument can be used to measure permeability
or hysteresis loops of soft ferrites.
Synthesis and characterization techniques Chapter - 3
3.47
3.5 Electrical Properties
(A) DC Resistivity
Introduction
There is a sense in which every property of a solid can be considered an
electrical property. This is because the particles that make up solids are
fundamentally electrical in nature. The response of solids to externally applied
electric fields is referring to as electrical properties.
When any substance is subject to an applied electric field E, a current of
electronic charge flows through the substance. The magnitude of the resultant
current density, j, is characterized by the electrical resistivity ρ or the electrical
conductivity (σ = 1/ρ) of the substance. The electrical resistivity and conductivity
are determined by:
j = σ E and E = ρ j
If the current density is measured in Am-2 and electric field (E) in Vm-1,
then the units of σ are Ω-1 m-1 or S m-1. The SI symbol of S stands for Siemens
not to be confused with ‘s’ for second. The units of resistivity are Ω m. for a
example of cross sectional area A and length L, the resistivity is related to the
electrical resistance R by ρ = RA / L Ω m
Electrical Resistivity
The range of resistivity values of ferrite and garnet materials is wide ranging from
10-4 to 109 Ω·m at room temperature [15]. In ferrites, the high value of resistivity
is associated with the simultaneous presence of ferrous (Fe2+) and ferric
(Fe3+)ions on equivalent lattice sites (usually the octahedral (B-) sites). The value
Synthesis and characterization techniques Chapter - 3
3.48
of resistivity in magnetite, Fe2+Fe23+O4 (Fe3O4), is of the order of 10
-4 or 10-5 Ω·m.
In nickel-zinc ferrite it was found that the resistivity was about 10 Ω·m when the
material contained 0.42 percent by weight of ferrous oxide but this resistivity
increased approximately one thousand fold when the specimen was more
completely oxidized.
A mechanism of conduction is known which covers the situation cited
above. The extra electron on a ferrous ion requires little energy to move to a
similarly situated adjacent ferric ion. The valence states of the two ions are
interchanged. Under the influence of an electric field, these extra electrons can
be considered to constitute the conduction current, jumping or hopping from one
iron ion to the next.
Since the materials are semiconductors, their resistivity ρ should decrease
with increase in temperature according to a relation of the form:
ρ= ρo exp (Eρ/kT)
Figure 3.18 The variation of resistivity (1) Nickel ferrite, (2) Copper ferrite and (3) Magnesium ferrite, with temperature.
This relation is indeed often observed and the activation energy E
then be interpreted as the energy required to
above. Some examples are given in Fig
between logρ versus 10
temperatures which correspond closely with the observed ferrimagnetic C
temperatures. As would be expected with such a conduction mechanism, the
high activation energy is associated with a high resistivity at room temperature.
In the electrical resistivity measurement a typ
Figure 3.19 specially
was used. It consists of two ceramic beads with supporting metal rods. The
electrodes E1 and E2
electrode (E2) is introduced into the c
the surface of the pellets. The brass electrode E
Figure 3.19 Sample holder
Synthesis and characterization techniques
This relation is indeed often observed and the activation energy E
then be interpreted as the energy required to cause the electron jump referred to
above. Some examples are given in Figure 3.18 which show the linear relation
versus 103/T. Breaks occur in the curves of
temperatures which correspond closely with the observed ferrimagnetic C
temperatures. As would be expected with such a conduction mechanism, the
high activation energy is associated with a high resistivity at room temperature.
In the electrical resistivity measurement a typical sample holder shown in
designed and fabricated for the resistivity measurement
was used. It consists of two ceramic beads with supporting metal rods. The
are also shown in this figure. The spring loaded brass
) is introduced into the ceramic beads and it pressed hard against
the surface of the pellets. The brass electrode E1 is fixed at the other end.
Sample holder for two-probe resistivity measurement.
Chapter - 3
3.49
This relation is indeed often observed and the activation energy Eρ can
cause the electron jump referred to
which show the linear relation
Figure 3.18 at
temperatures which correspond closely with the observed ferrimagnetic Curie
temperatures. As would be expected with such a conduction mechanism, the
high activation energy is associated with a high resistivity at room temperature.
ical sample holder shown in
designed and fabricated for the resistivity measurement
was used. It consists of two ceramic beads with supporting metal rods. The
are also shown in this figure. The spring loaded brass
eramic beads and it pressed hard against
is fixed at the other end.
probe resistivity measurement.
Synthesis and characterization techniques Chapter - 3
3.50
The resistance of a pellet was measured by two terminal method using
meg-ohm meter. The sample surfaces were rubbed by graphite and thin
aluminium foils were placed between the terminals of sample holder and the
pellet surfaces for the proper contacts. The sample holder with the pellet was
placed in a horizontal electric furnace to study the change in resistivity with
temperature. The temperature of the furnace was controlled by maintaining the
current passing through the heater by means of current controller. The
temperature of the sample was measured with Cr-Al thermocouple. Experimental
set-up is shown in the Figure 3.20. The resistance of the each pellet was
measured for raising and falling of temperature at the gap of 20˚C. The thickness
(l) and diameter of the pellets were measured by digital vernier calipers. From
these observations the resistivity (ρ) was found us. Logarithm of resistivity was
plotted against reciprocal of temperature (103/T). The activation energies for the
ferrimagnetic region (Ef) and paramagnetic region (Ep) in electron volt (eV) were
determined from the slopes of these plots.
Figure 3.20 Experimental set
Hopping model of electrons
Jonker has observed in cobalt ferrites that the transport properties differ
considerably from those of normal semiconductors, as
free to move through the crystal lattice but jump from ion to ion. It was also noted
that in this type of materials the possibility exists of changing the valency of a
considerable fraction of metal ions and especially that of
Assuming the number of electrons contributing to be equal to the
number of Fe2+ ions and the number electron holes to be equal to the number of
Co3+ ions Jonker has calculated from the resistivity data extremely low values of
mobilities µ1 = 10-4 cm
Further, even for samples with a large concentration of Fe
strong exponential dependence of resistivity on temperature was found. From the
ordinary band theory of conduction one would expect metallic behaviour for such
Synthesis and characterization techniques
Experimental set-up for dc resistivity measurement
Hopping model of electrons
Jonker has observed in cobalt ferrites that the transport properties differ
considerably from those of normal semiconductors, as the charge carriers are not
free to move through the crystal lattice but jump from ion to ion. It was also noted
that in this type of materials the possibility exists of changing the valency of a
considerable fraction of metal ions and especially that of iron ions
Assuming the number of electrons contributing to be equal to the
ions and the number electron holes to be equal to the number of
ions Jonker has calculated from the resistivity data extremely low values of
cm2/Vsec for electrons and µ2 = 10-8 cm2/V sec for holes.
Further, even for samples with a large concentration of Fe2+ or Co
strong exponential dependence of resistivity on temperature was found. From the
ordinary band theory of conduction one would expect metallic behaviour for such
Chapter - 3
3.51
easurement.
Jonker has observed in cobalt ferrites that the transport properties differ
the charge carriers are not
free to move through the crystal lattice but jump from ion to ion. It was also noted
that in this type of materials the possibility exists of changing the valency of a
[16].
Assuming the number of electrons contributing to be equal to the
ions and the number electron holes to be equal to the number of
ions Jonker has calculated from the resistivity data extremely low values of
/V sec for holes.
or Co3+ions, a fairly
strong exponential dependence of resistivity on temperature was found. From the
ordinary band theory of conduction one would expect metallic behaviour for such
Synthesis and characterization techniques Chapter - 3
3.52
high concentration, i.e. a high mobility with only slight temperature dependence.
In cobalt ferrite compounds the behaviour is similar to NiO and Fe2O3 and the
ordinary theory based on simple band picture does not apply. The activation
energy does not belong to the energy picture of electrons but to the crystal lattice
around the site of electrons. The general expression for the total conductivity
where we have two types of charge carriers can be given as [17]
σ = n1eµ1 + n2eµ2
The temperature dependence of conductivity arises only due to mobility and not
due to the number of charge carriers in the sample.
Thus, we can conclude that, for the hopping conduction mechanism
1. Low value of mobility.
2. Independence of Seebeck coefficient on temperature. This property is
due to the fact that in hopping model the number of charge carriers is
fixed.
3. Thermally activated process with activation energy Ea called the hopping
activation energy.
4. Occurrence of n-p transition with changes in the Fe2+ or oxygen
concentration in the system.
Small polaron model
A small polaron is a defect created when an electronic carrier becomes trapped
at a given site as a consequence of the displacement of adjacent atoms or ions.
The entire defect (carrier plus distortion) then migrates by an activated hopping
mechanism. Small polaron formation can take place in materials whose
Synthesis and characterization techniques Chapter - 3
3.53
conduction electrons belong to incomplete inner (d or f) shells which due to small
electron overlap; tend to form extremely narrow bands. The possibility for the
occurrence of hopping conductivity in certain low mobility semiconductors,
especially oxides, has been widely recognized for some time.
The polaron comprises the electron plus its surrounding lattice
deformation. (Polaron can also be formed from holes in the valence band). If the
deformation extends over many lattice sites, the polaron is “large”, and the lattice
can be treated as a continuum. Charge carriers inducing strongly localized lattice
distortions form “small” polarons. The concept of large polaron is most useful
when the carrier mobility is high and the carrier density and temperature both are
low [18].
For a small polaron the spatial extent of its self-trapped charge is
comparable to or smaller than interatomic distances. In particular atoms
surrounding an excess charge are displaced to new equilibrium positions and
produce a potential well which traps the excess particles. Small polaron
formation is typically associated with the interaction of the excess charge with the
atoms in its immediate vicinity. Thus, unlike the case of the large polaron, the
self-trapping is not primarily associated with the long range interaction of an
excess charge with the dipolar fields of polar materials. Hence, the name
polaron, coined to reflect this latter situation, is a misnomer for the small polaron.
Electron and hole small polarons are found in both polar and non-polar
semiconductors and insulators. This includes numerous oxides and molecular
solids.
Synthesis and characterization techniques Chapter - 3
3.54
Small polaron motion proceeds relatively slowly via a succession of
phonon-assisted hopping events. As a result, the small polaron drift mobility
increases as a thermal agitation of the solid increases. Above a temperature
comparable to the solid’s phonon temperature, the diffusivity increases in an
Arrhenius manner with reciprocal temperature.
The migration of small polaron requires the hopping of both the electron
and the polarized atomic configuration from one site to an adjacent one [16]. For
fcc lattice the drift mobility takes the form
µ = (1 – c) e a2Γ/kT
where, e is the electronic charge, a the lattice parameter, c is the fraction of sites
which contain an electron (c=n/N), n is the number of electrons and N the
number of available sites per unit volume. The quantity Γ is the jump rate of the
polaron form one site to a specific neighbouring site.
The small polaron model also explains the low value of mobility,
temperature independent Seeback coefficient and thermally activated hopping. In
addition to these properties if the hopping electron becomes localized by virtue of
its interaction with phonons, then a small polaron is formed and the electrical
conduction is due to hopping motion of small polarons.
(B) Thermo electric power measurement
Introduction
The temperature difference between the two ends of a semiconductor gives rise
to an electro motive force (emf) known as thermo emf (∇V). It is found that the
Synthesis and characterization techniques Chapter - 3
3.55
generated thermo emf is proportional to the temperature difference (∆T) and is
given by the relation
∇V = α ∆T (1)
where, α is the Seebeck coefficient also often known as the thermo-electric
power.
Hall effect and thermo-electric power study are widely used in the
interpretation of the conduction mechanism in semiconductors. The interpretation
of the Hall effect is more straight forward, and it also gives precise results.
However, in the case of low mobility materials such as ferrites, garnets and
perovskites, it is sometimes difficult to measure the Hall effect; in such cases the
thermo-electric power measurement is the only alternative. The measurement of
thermo-emf is simple and its sigh gives vital information about the type of
conduction (p-type or n-type) or charge carriers (electrons or holes) responsible
for the electrical conduction in semiconductors. Another important significance of
thermo-emf is that, it enables one to calculate the values of Fermi energy and
carrier concentration. A knowledge of Fermi energy helps in the determination of
the various regions viz. impurity conduction, impurity exhaustion and intrinsic
conduction regions of a semiconductor.
In the case of a n-type semiconducting material, the hot surface becomes
positively charged, as it loses some of its electrons. The cold surface of the
semiconductor becomes negatively charged due to the diffusion of free electrons
from the hot portion. Conversely, in a p-type semiconducting material, the hot
surface becomes negative, and the cold one positive. Thus the type of
Synthesis and characterization techniques Chapter - 3
3.56
conduction in a given semiconducting material can readily be determined from
the sign of the thermo-emf.
Theory
The Fermi energy in the case of a semiconductor can be obtained from the
relation
α T = (EG – EF) + 2kT (2)
for n-type semiconductors and
αT = EF + 2kT (3)
for p-type semiconductors.
where, EG = Energy gap of the ferrite semiconductor,
EF = Height of the Fermi energy level from the top of the filled Valence band
2kT = the term which accounts for the transfer of kinetic energy of the carriers in
moving from the hot region of the ferrite to a cold one.
While discussing the electrical properties of α – Fe2O3, for which the
mobility of the charge carrier is low, Morin [19] assumed that the conduction is
occurring in exceedingly narrow bands or in localized levels. This assumption
leads to the result that the kinetic energy term in the Seebeck effect can be
neglected, so that for electrons alone,
α T = EG – EF (4)
while,for holes alone,
α T = EF (5)
Experimental procedure
The experimental set-up to determine thermo
Figure 3.21. It consists of a point contact probe, which acts as a hot junction and
a base which acts as a cold junction. Between the two junctions a sample is kept.
The temperature of the hot probe is raised to a maximum of around
the help of an electric h
Figure 3.21 Photograph of thermo electric power measurement set up
A thermoelectric power study was carried out over a temperature range
300–473 K by the differential method. The temperature gradient was meas
by two chromel-alumel thermo
while the thermo-emf was measured with the help of a digital micro voltmeter
with an accuracy of ±3%. In order to achieve good thermal stability, the values of
the thermo-emf have been recorded while cooling. The sample is maintained at a
given temperature for about 5
Synthesis and characterization techniques
rocedure
up to determine thermo-emf of ferrite samples is shown in
It consists of a point contact probe, which acts as a hot junction and
a base which acts as a cold junction. Between the two junctions a sample is kept.
The temperature of the hot probe is raised to a maximum of around
the help of an electric heater, which is wound round the hot probe.
Photograph of thermo electric power measurement set up
A thermoelectric power study was carried out over a temperature range
473 K by the differential method. The temperature gradient was meas
alumel thermo-couples that were kept very close to the sample
emf was measured with the help of a digital micro voltmeter
with an accuracy of ±3%. In order to achieve good thermal stability, the values of
have been recorded while cooling. The sample is maintained at a
given temperature for about 5-10 minutes.
Chapter - 3
3.57
samples is shown in
It consists of a point contact probe, which acts as a hot junction and
a base which acts as a cold junction. Between the two junctions a sample is kept.
The temperature of the hot probe is raised to a maximum of around 473K with
eater, which is wound round the hot probe.
Photograph of thermo electric power measurement set up.
A thermoelectric power study was carried out over a temperature range
473 K by the differential method. The temperature gradient was measured
couples that were kept very close to the sample
emf was measured with the help of a digital micro voltmeter
with an accuracy of ±3%. In order to achieve good thermal stability, the values of
have been recorded while cooling. The sample is maintained at a
Synthesis and characterization techniques Chapter - 3
3.58
A pointed hot probe is used here since ferrite samples are very good
thermal conductors; if a pointed probe is not used to upper and the lower
surfaces of the samples will attain almost the same temperature and no
temperature gradient will be maintained between them.
Synthesis and characterization techniques Chapter - 3
3.59
References
1. S. T. Alone and K. M. Jadhav
Parmana J. Phys. 70(1) (2008) 173.
2. R C Weast (Ed.) and M J Astle (Assoc. Ed.)
Handbook of Chaemistry and Physics CRC Press Inc. (Florida) 1981.
3. A. Verma, T. C. Goel, R. G. Mendiratta and R. G. Gupta, J. Magn. and
Magn. Mater.192(2)(1999) 271.
4. H. M. Rietveld, J. Appl. Cryst. 2 (1969) 65.
5. H. M. Rietveld, Acta, Cryst 22 (1967) 151.
6. J. Rodriquez-Cravajal, Physica B, 192 (1993) 55.
7. L. B. McCusker, R. B. Von Dreele, D. E. Cox, D. Louer and P. Scardi,
J. Appl Cryst. 32 (1999) 36.
8. R. A. Young, “The Rietveld Method”, Oxford University Press Inc (1993).
9. Ian. M. Watt, “The Principles & Practice of Electron Microscopy”, 2nd Ed.,
Cambridge University Press (1997)89.
10. Elton. N. Kaffmann, “Characterization of Materials”, John Wiley & Sons,
Inc., Hoboken, New Jersey, Vol. 2 (2003).
11. A. P. Murani, J Magn. Magn. Mater., 5 (1977) 95.
12. K. J. Standley, “Oxide Magnetic Materials”, Clerendon Press, Oxford,
(1962).
13. C. Radhakrishnamurthy, S. D. Likhite, E. R. Deutsch and G. S. Murthy,
Phys. Earth and planetary Interiors, 26 (1981) 37.
Synthesis and characterization techniques Chapter - 3
3.60
14. C. Radhakrishnamurthy S. D. Likhite and S. P. Sastry, “Philosophical
Magazine”, 23 (1971) 503.
15. K.J. Standly, “Oxide Magnetic Materials”, Oxford, (1962).
16. G. H. Jonker, J.Phys,Chem. Solids,9 (1959)165.
17. B. Vishwanathan and V.R.K. Murthy, Ferrite materials: Science and
Technology, 29 (1990).
18. S. L. Kakani and C. Hemrajani, Text book of Solid State Physics, Sultan
Chand (1997).
19. F. J. Morin, Phys. Rev., 93(1953)1195.